This work is devoted to one special sort of games, studied with theory of games. A subject matter of this theory is situations where several sides participate, and every of sides pursues its own goal. The result, or final state of situation, is defined with joint actions of all sides. These situations are called games.

Theory of games explore the possibilities of colliding sides and attempts to define such strategy for every player that the result of the whole game would be best in certain sense, called principle of optimality (we consider Nash principle of optimality).

The main aim of current work is finding criterion conditions for existing a Nash equilibrium situations in mixed expansion of game with ordered outcomes. In part I we set a connection between Nash equilibrium situations and balanced submatrixes of payoff function’s matrix. In part II we found required and sufficient conditions for balanced matrix. In appendix there is a program for finding a Nash equilibrium situations in arbitrary finite game of two players with ordered outcomes.